Crack Paths 2006

the crack tip approaches and crosses the interface. A muchsmaller discontinuity appears

for the Al upper/ P M M lAower case. These numerical values of the bimaterial SIF 3PB

tests where used in the fatigue crack growth analysis by assuming that ' Kis equal to

the K1max SIF solution under pure bending constant amplitude loads.

Figure 4 is showing the stress distribution for P M M uApper/Al lower around the

crack tip using a normalised crack of a/W = 0.4, which relates to crack approaches the

interface. In this Figure, the normal stress in the longitudinal direction (Vx) and the

lateral direction (Vy) are illustrated as contour maps. The interface is assumed to be

perfectly bonded, and hence Vy is shown continues across the interface while Vx is

discontinues. Since the crack tip approaches the interface, the value of Vx at the point

just above the interface becomes compressive. This compressive stress may turn into a

positive residual stress when unloading occurs during the fatigue test and therefore, this

could lead to a crack initiation inside the P M M (Aupper) region. In other words, a

highly compressive stress just upper of the interface may trigger a “crack jump” as

observed in the experiments.

a P

B

W/2

P M M A

a.

Al

c.

S

0.010

b. b.

P M M A

-0.5

crack tip

0

0.005 0.01 0.015

0 0.02

-1

0

0.5

-1

0.005

1

-0.5

0

0

1.5

-1.5

interface

2

-0.0101050

0

0

-1.5

-0.005

-1

-0.5

Al

-0.010

0

0.005 0.01

0.015

0.02

x 3 / 2 2 u V

P S B W

P S B W y 3 / 2 2 u V

Figure 4. Distribution of stresses due to perpendicular crack (Wa/= 0.4)

approaching the bimaterial interface; a. Illustration of specimen where the hatching

and; c. Contours

V

area represents the modelled area; b. Contours of

u

2

B W

3/

PS

x

2

B W y u2 32/ V

of

PS . (Grey region represents positive stress).